If you prefer to use Google as the default search engine in the windows phone 8 internet explorer app, you can change the default search engine through the application settings options.
On the phone, go to SETTINGS and swipe over to the “applications” screen. Then tap Internet Explorer
Tap the “advanced settings” button on the Internet Explorer screen
Scroll down the ADVANCED SETTINGS screen and tap the white space under “Default search provider” to change from the default of Bing to Google.
The Search button on the phone will still bring up and use Bing and you can’t reassign that button to use Google.
But if you can open the Internet Explorer app from the programs screen (or from a pinned tile on your start screen), you can input your search terms in the white address bar on the bottom of the screen to search via the Google search engine.
Please Note: This option may not be available for all makes and models of Windows Phone 8.